Patrick wrote, "The logarithm is not a unit of measure. It is a transformation of units of measure. The log of average anual income is not the same unit as the log of annual rainfall. The log of illumination to which platinum paper is sensitive is not the same as the log of illumination which the normal eye sees or the log of the illumination to which pan film is sensitive."
Patrick, yes, a logarithm is not a unit of measurement. An LogE is a unit of measure.
Thanks for the catch - I'll fix my comment above to reflect this.
Patrick - I just looked it over, and I did not change anything above.
I agree, a log is not a unit of measure. But a logE is a unit of measure of light.
"The log of average anual income is not the same unit as the log of annual rainfall."
Sure, but are you saying we can't graph two items against each other? You know that is not true. We can even graph items where the units do not match - take a look at most any graph out there. Salery($) vs. Age (Time), Concentration (mg/L) vs. Absorbance (Abs.), Development Time (Time) vs. Temp (Temp). The combinations of differing units is nearly endless. We can very most certainly graph LogE in UV vs LogE in Visual. There is no problem there.
"The log of illumination to which platinum paper is sensitive is not the same as the log of illumination which the normal eye sees or the log of the illumination to which pan film is sensitive."
YES - this is exapctly my point. The data on the x-axis only relates to the exposure that was given to the piece of panchromatic film. It does not and cannot relate to the exposure that was given to the platinum paper. They are unrelated exposures. And because of that we can use logE of visual light for our x-axis and plot it against our logE of UV light for our platinum print.
We are simply measuring and graphing "input" vs. "response".
Our step wedge controls the exposure on the film and then the processed film with steps on it controls the exposure on our platinum paper. Each expsoure is completely unrelated and that is exactly why we need to carefully consider the conditions and the sensitivity of our materials in each of these two steps. The UV light is not shining through our step wedge and then onto our Pt paper. There is another step invloved there and that is the creation of our negative. The UV light shines through the negative that we made, not the original step wedge. That's why the original step wedge MUST be measured with the visual channel on the densitometer.
Patrick, do you have any thoughts on my IR film/Pt paper example above? I would be interested in hearing it.
Once again, the logE units on the x and y axis are relative, not absolute and the thing that links them for the purpose of graphing is the measuring instrument that is used to measure the step tablet and the tests strips produced from it. Nothing else. If you mix values (i.e. different measuring system) you will get apple to oranges units of measurement, assuming that the step tablet is not absolutely neutral in color. If you measure the step tablet in Blue mode and the test strips in Blue mode each unit of density will occupy the same physical distance on the graph. If you measure the step tablet in UV mode and the test strips in UV mode each unit of density will occupy the same physical space on the x and y axis. If you do anything else the units of distance will be of different length on the x and y axis.
Originally Posted by Kirk Keyes
About the charts, this is no conundrum. Since, as you correctly surmise, the same step tablet values were used for the Visual, Blue and UV curves, the UV curve is not correct. Assuming a step tablet with different Visual and UV values was used for the plotting of those, as I think was the case, the UV curve should have a steeper slope. When I prepared those curves I assumed that that the Stouffer step tablet used to expose the film was of neutral color and almost certainly measured it in Visual mode. I now realize that it is not.
I have considered the IR film/Pt/Pd scenario you describe. It is not relevant to my point because you are not using IR light to expose the Pt/Pd. print. You can expose the film with any light to which it has sensitivity and will get an exposure. You could do this with red, green, blue, ultraviolet or infrared, either by using light of that spectrum or using appropriate cut-off filters. This will no doubt result in negatives of different contrast and density but it will have little if any affect on graphing. In other words, whatever light you use to expose the film the densities could potentially read differently if the film is not neutral in color according to the spectral sensitivity of the measuring instrument.
This discussion has been interesting. I had been vaguely aware of the issue for some time but when the discussions began there were some questions in my own mind as to what would be the correct procedure when dealing with a step tablet that did not measure the same in Visual, Blue and UV mode. Having now worked through the situation more thoroughly, and having heard everything that has been said by many people whose opinions and knowledge I respect, I am convinced that I am right, not about everything of course but yes with regard to how the step tablet should be measured.
I would not preclude revisiting the issue at some point in the future but for now I am satisfied that I have nothing more to add. Folks will just have to read the messages for themselves and come to their own conclusion. But my position is that if you donít agree with me we will just have to agree to disagree.
Last edited by sanking; 08-12-2004 at 04:32 PM. Click to view previous post history.
I've used logarithms a LOT, having been in the "pre-PC" era. Heavens to Betsy, I have memories of Pickett Slide Rules, constructed with the basic idea of logarithmic scales ... and I've made more than a few pencil-and paper calculations (slide rule-less) with them.
Now ... I know how to use them ... how the squat do I describe what they are? ... try: (cheating), "The power to which a fixed number, called the base, must be raised in order to produce a given number, the antilogarithm."
In use, to mulitply 2 X 3: one would determine the log of 2; (determining both mantissa and characteristic) and the log of 3; add them together; and determine the antilog of the sum - which would be something like 5.9999999999999999.
The "base" could be ... commonly 2, 10 ... or "e" (small "e" = 2.7182818284+) - not to be confused with capital "E" ... which represents "Exposure".
"LogE" indicate the use of a logarithmically drawn graph, to plot the value of the exposure - whatever that was - in logarithmic terms.
Wow... what a memory exercise this has been. This is equal to trying to remember how to calculate square .. or cube roots - by hand!!
Ed Sukach, FFP.
[QUOTE=Ed Sukach]I've used logarithms a LOT, having been in the "pre-PC" era. Heavens to Betsy, I have memories of Pickett Slide Rules, constructed with the basic idea of logarithmic scales ... and I've made more than a few pencil-and paper calculations (slide rule-less) with them. "
I still have a 7" circular slide rule I called a slip disk. It is equivalent to about a 25" straight one and has all the log, trig square root and even cube root scales. I remember using 10 place log and trig tables to do calculations for topographic computing. The only desk calculators we had were adding machines. Later, Marchant and Friden made electromechanical desk calculators. Try inverting a 10X10 matrix on one of those. When I retired from NASA, we still did not have desk top PC's and the main frame that did much of the data reduction was limited. A fellow doing theoretical analysis of loads on helicopter rotors came to me one day saying he had to invert a 250 X250 matrix and the main frame couldn't do it. The computing time for the solution was over 80 hours, and that was greater than the mean time between failures of the IBM 7094 we had. When I left, we had graduated to an early Cray super computer, and last time I visited all the engineers had desk terminals.
Ain't life grand?
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Interesting thread and Iím quite pleased to see it unfold unemotionally as seems to happen on other forums.
I donít practice BTZS, nor am I very familiar with WinPlotter though I do have the software.
When I first started reading this I was thinking that Sandyís logic was correct, but after reading Kirkís replies and thinking about this, Iím in agreement with Kirk.
Here why: Forget WinPlotter for a moment. If we were charting an H-D curve we would place LogE (exposure) on the X axis and LogD (density) on the Y. Instead of using a step tablet, letís say we actually made 21 separate exposures on 21 sheets of film. We would then have 21 unique exposures to plot on the X axis along with 21 densities to plot on Y. Now weíre not using individual exposures, but simulating exposures using a step tablet, hence the reason WinPlotter need to know the densities of the step wedge used to expose the test film Ė so it can calculate the exposures. For this reason Kirkís explanation sounds most logical: the step wedge needs to be read with the same light thatís used to make the initial exposure on film.
Patrick wrote: "I still have a 7" circular slide rule I called a slip disk."
Patrick, could you leave that to me in your will? :^) I love those things too. Who would have thought that scratching a bunch of lines based on logarithms would make such powerful calculating device. I have an aluminum Pickett and a Ivory and Mahogany K&E. But I haven't gotten a nice circular slide rule yet...
Ed, thanks for the refresher on logarithms for those that are not familiar with them. I was trying myself to remember what the number in front of the decimal was called earlier today and you have it here - the characteristic!
Thanks for adding to the thread! I'm glad that people are finding this subject interesting as this really covers a very fundamental issue and I'm kind of suprised that there is so much confusion on this.
You have made a very important point here, one that I overlooked. As I have been trying to point out from the beginning, the two axis on an H&D graph do not diplay the same information, and therefore there is no need that the units need to actually match. I believe that everyone is getting confused because at first glance, it seems like the units are exactly the same, and therefore that is why everyone is wanting to use the same units. But you are right, what we are really graphing on one of these charts are Exposure vs. Density. Nothing more, nothing less. We actually use the log of the Exposure and the log of the Density, and perhaps that is adding an extra layer of confusion to the issue, but the log part really does not matter as we only do that to make the graphs look nicer (and to make our doublings of numbers produce straight lines). But the log part does not matter, we could make these graphs without using logs.
Even the letters of the name of these types of graphs should have pointed this out to us - they are H&D graphs. H represents the Exposure given to the film, and D is the Density of that processed film. So we are not plotting the same units on the graph - we need to recognize this.
Pete, your example makes an excellent case and it does prove the point I'm making, in yet one more way.
... And, lest we forget ... Tables of Involutes. I did a lot of work with gearing .. calibrating Master Gears, and working with "Special" tooth forms.
We worked a LOT with Space Optics .. and sundry other "parts" that went up, never to come down again - and come to think of it .. some that went down, and HOPEFULLY did come up again (DSRV - Deep Sumbergenge R... (reasearch???) Vehicle....
My "Axe" was a Fifteen-Place Curta Calculator ... a much refined, hand-held Babbage Engine. Made at Vaduz, Lichtenstein. Never failed ... completely mechanical.
You know .. compared to the "Wimp" Engineers of today (sit there and push a few buttons)... we did truly *marvelous* work..
Ed Sukach, FFP.
You described it *VERY* well, Kirk.
Originally Posted by Kirk Keyes
Only ... The letters stand for (H)urter and (D)riffield, two guys who did a bunch of work in trying to determine a standard way for expressing film speed.
There was a H&D film speed; a Weston speed. and finally ASA, which morphed to ISO.
Ed Sukach, FFP.